Details

analyze462.0ms (5.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	176×	body	128	valid
8.0ms	32×	body	2048	valid
4.0ms	23×	body	1024	valid
4.0ms	12×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify236.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 34.1b

Counts

2 → 1

Compiler

Compiled 66 to 54 computations (18.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_423`
10×	`add-log-exp_binary64_462`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
8×	`add-sqr-sqrt_binary64_445`
7×	`add-cube-cbrt_binary64_458`
6×	`distribute-lft-out_binary64_374`
5×	`times-frac_binary64_429` `pow1_binary64_484` `associate-/l*_binary64_368`
3×	`sqrt-prod_binary64_439` `distribute-rgt-neg-in_binary64_381`
2×	`sqrt-div_binary64_440` `flip-+_binary64_397` `associate-+l-_binary64_358` `neg-sub0_binary64_418` `flip3--_binary64_427` `associate-/l/_binary64_370` `flip3-+_binary64_426` `flip--_binary64_398` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`
1×	`sub-neg_binary64_416` `diff-log_binary64_515` `neg-log_binary64_516` `cancel-sign-sub-inv_binary64_389` `prod-exp_binary64_472` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`

Counts

4 → 70

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
13.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series511.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
125.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
62.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5290	1826

prune447.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 6.8b

Counts

83 → 9

Compiler

Compiled 8216 to 5886 computations (28.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) a)))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite112.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

693×	`times-frac_binary64_429`
439×	`add-sqr-sqrt_binary64_445`
364×	`*-un-lft-identity_binary64_423`
290×	`add-cube-cbrt_binary64_458`
74×	`difference-of-squares_binary64_392`
71×	`associate-/r*_binary64_367`
40×	`sqrt-prod_binary64_439`
37×	`distribute-lft-out--_binary64_375`
25×	`add-exp-log_binary64_461`
17×	`div-inv_binary64_420`
15×	`div-exp_binary64_474`
13×	`add-cbrt-cube_binary64_459`
8×	`add-log-exp_binary64_462`
6×	`pow1_binary64_484` `cbrt-undiv_binary64_457`
5×	`associate-/r/_binary64_369`
4×	`cancel-sign-sub-inv_binary64_389`
3×	`rec-exp_binary64_473` `1-exp_binary64_467` `flip3--_binary64_427` `flip--_binary64_398` `associate-/l*_binary64_368`
2×	`sqrt-div_binary64_440` `sub-neg_binary64_416` `diff-log_binary64_515`
1×	`rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `inv-pow_binary64_508`

Counts

4 → 356

Calls

4 calls:

30.0ms	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) a)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series500.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 1 (/.f64 2 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b) a)))
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify177.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4953	16303
1	4953	16303

prune975.0ms (12%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	366	2	368
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	368	9	377

Merged error: 6.8b

Counts

377 → 9

Compiler

Compiled 15016 to 9525 computations (36.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
3.2b	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
11.3b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite70.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
34×	`times-frac_binary64_429` `add-sqr-sqrt_binary64_445`
33×	`*-un-lft-identity_binary64_423`
17×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
14×	`associate-/l*_binary64_368`
13×	`add-cube-cbrt_binary64_458` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
11×	`sqrt-prod_binary64_439`
10×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392`
8×	`add-log-exp_binary64_462` `associate-/r*_binary64_367`
6×	`cancel-sign-sub-inv_binary64_389` `associate-/r/_binary64_369`
5×	`pow1_binary64_484` `flip3--_binary64_427` `flip--_binary64_398` `distribute-rgt-neg-in_binary64_381`
4×	`div-inv_binary64_420`
2×	`sqrt-div_binary64_440` `diff-log_binary64_515` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`sub-neg_binary64_416` `associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 125

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
19.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series971.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
318.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
136.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify101.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4940	4228
1	4940	4228

prune342.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	2	4	6
Picked	1	0	1
Done	1	1	2
Total	137	9	146

Merged error: 6.7b

Counts

146 → 9

Compiler

Compiled 6944 to 4494 computations (35.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.1b	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
3.2b	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite73.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_445`
36×	`*-un-lft-identity_binary64_423`
34×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
27×	`associate-r_binary64_363`
24×	`times-frac_binary64_429`
20×	`add-cube-cbrt_binary64_458`
12×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
10×	`sqrt-prod_binary64_439` `pow1_binary64_484`
9×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
8×	`distribute-lft-out--_binary64_375` `difference-of-squares_binary64_392` `add-log-exp_binary64_462`
6×	`cancel-sign-sub-inv_binary64_389`
4×	`distribute-rgt-neg-in_binary64_381`
3×	`pow-prod-down_binary64_494` `flip3--_binary64_427` `flip--_binary64_398` `associate-/r*_binary64_367`
2×	`sqrt-div_binary64_440` `diff-log_binary64_515` `associate-*r/_binary64_365` `associate-/r/_binary64_369` `div-inv_binary64_420`
1×	`sub-neg_binary64_416` `associate-l_binary64_364` `associate--l-_binary64_361` `neg-log_binary64_516` `rem-sqrt-square_binary64_436` `neg-sub0_binary64_418` `associate-/l/_binary64_370` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `associate-/l_binary64_368`

Counts

4 → 113

Calls

4 calls:

24.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
19.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
11.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series951.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
310.0ms	(/.f64 (.f64 (.f64 a 2) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))) a)
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
121.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4937	3223
1	4937	3223

prune226.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	125	9	134

Merged error: 6.7b

Counts

134 → 9

Compiler

Compiled 4703 to 2868 computations (39% saved)

regimes192.0ms (2.4%)

Compiler: Compiled 740 to 590 computations (20.3% saved)

bsearch114.0ms (1.4%)

Steps

Iters	Range	Point
10	1.6829726428472436e+90	9.502704283103217e+100	7.7377607878944895e+96
9	-2.0073421179495267e-256	-1.6377269175435972e-261	-7.621813580046727e-260
9	-7.464578554549161e+98	-1.7868669415526677e+91	-1.3138164296877506e+98

Iters

Range

Point

1.6829726428472436e+90

9.502704283103217e+100

7.7377607878944895e+96

-2.0073421179495267e-256

-1.6377269175435972e-261

-7.621813580046727e-260

-7.464578554549161e+98

-1.7868669415526677e+91

-1.3138164296877506e+98

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	87
1	119	87

end0.0ms (0%)

sample1.4s (17.3%)

Algorithm

1×

intervals

Results

279.0ms	1093×	body	2048	valid
272.0ms	5224×	body	128	valid
141.0ms	712×	body	1024	valid
140.0ms	427×	body	4096	valid
57.0ms	362×	body	512	valid
32.0ms	654×	body	128	nan
20.0ms	389×	body	128	invalid
18.0ms	182×	body	256	valid

Compiler

Compiled 251 to 192 computations (23.5% saved)

Details

analyze462.0ms (5.7%)

sample38.0ms (0.5%)

simplify236.0ms (2.9%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite44.0ms (0.5%)

series511.0ms (6.3%)

simplify57.0ms (0.7%)

prune447.0ms (5.5%)

localize13.0ms (0.2%)

rewrite112.0ms (1.4%)

series500.0ms (6.1%)

simplify177.0ms (2.2%)

prune975.0ms (12%)

localize13.0ms (0.2%)

rewrite70.0ms (0.9%)

series971.0ms (11.9%)

simplify101.0ms (1.2%)

prune342.0ms (4.2%)

localize15.0ms (0.2%)

rewrite73.0ms (0.9%)

series951.0ms (11.7%)

simplify77.0ms (0.9%)

prune226.0ms (2.8%)

regimes192.0ms (2.4%)

bsearch114.0ms (1.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.4s (17.3%)

Profiling